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2001/2002 A Diagonalization Property between Hurewicz and Menger
Boaz Tsaban
Real Anal. Exchange 27(2): 757-764 (2001/2002).


In classical works, Hurewicz and Menger introduced two diagonalization properties for sequences of open covers. Hurewicz found a combinatorial characterization of these notions in terms of continuous images. Recently, Scheepers has shown that these notions are particular cases in a large family of diagonalization schemas. One of the members of this family is weaker than the Hurewicz property and stronger than the Menger property, and it was left open whether it can be characterized combinatorially in terms of continuous images. We give a positive answer. We also find some additivity numbers for these classes. This paper can serve as an exposition of this fascinating subject.


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Boaz Tsaban. "A Diagonalization Property between Hurewicz and Menger." Real Anal. Exchange 27 (2) 757 - 764, 2001/2002.


Published: 2001/2002
First available in Project Euclid: 2 June 2008

zbMATH: 1044.26001
MathSciNet: MR1923165

Primary: 03E75 , 26A03 , 37F20

Keywords: continuous images , Hurewicz property , Menger property , Selection principles

Rights: Copyright © 2001 Michigan State University Press

Vol.27 • No. 2 • 2001/2002
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